z^2-(2+i)z+(3+i)=0

Solution for z^2-(2+i)z+(3+i)=0 equation:

Simplifying
z2 + -1(2 + i) * z + (3 + i) = 0

Reorder the terms for easier multiplication:
z2 + -1z(2 + i) + (3 + i) = 0
z2 + (2 * -1z + i * -1z) + (3 + i) = 0

Reorder the terms:
z2 + (-1iz + -2z) + (3 + i) = 0
z2 + (-1iz + -2z) + (3 + i) = 0

Remove parenthesis around (3 + i)
z2 + -1iz + -2z + 3 + i = 0

Reorder the terms:
3 + i + -1iz + -2z + z2 = 0

Solving
3 + i + -1iz + -2z + z2 = 0

Solving for variable 'i'.

Move all terms containing i to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + i + -1iz + -2z + -3 + z2 = 0 + -3

Reorder the terms:
3 + -3 + i + -1iz + -2z + z2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + i + -1iz + -2z + z2 = 0 + -3
i + -1iz + -2z + z2 = 0 + -3

Combine like terms: 0 + -3 = -3
i + -1iz + -2z + z2 = -3

Add '2z' to each side of the equation.
i + -1iz + -2z + 2z + z2 = -3 + 2z

Combine like terms: -2z + 2z = 0
i + -1iz + 0 + z2 = -3 + 2z
i + -1iz + z2 = -3 + 2z

Add '-1z2' to each side of the equation.
i + -1iz + z2 + -1z2 = -3 + 2z + -1z2

Combine like terms: z2 + -1z2 = 0
i + -1iz + 0 = -3 + 2z + -1z2
i + -1iz = -3 + 2z + -1z2

Reorder the terms:
3 + i + -1iz + -2z + z2 = -3 + 2z + -1z2 + 3 + -2z + z2

Reorder the terms:
3 + i + -1iz + -2z + z2 = -3 + 3 + 2z + -2z + -1z2 + z2

Combine like terms: -3 + 3 = 0
3 + i + -1iz + -2z + z2 = 0 + 2z + -2z + -1z2 + z2
3 + i + -1iz + -2z + z2 = 2z + -2z + -1z2 + z2

Combine like terms: 2z + -2z = 0
3 + i + -1iz + -2z + z2 = 0 + -1z2 + z2
3 + i + -1iz + -2z + z2 = -1z2 + z2

Combine like terms: -1z2 + z2 = 0
3 + i + -1iz + -2z + z2 = 0

The solution to this equation could not be determined.